few_shots: Example:
Problem/activity:
For each pair of numbers, determine if the values are equivalent. Explain your reasoning for each one.
a.
$$-0.25$$
and
$$\frac{1}{-4}$$
b.
$$-\left ( \frac{1}{4} \right )$$
and
$$\frac{-1}{-4}$$
c.
$$\frac{-1}{4}$$
and
$$-\frac{1}{4}$$


Mathematical concept/skill options: 
A. Apply and extend previous understandings of operations with fractions to add, subtract, multiply, and divide rational numbers.
B. Reason quantitatively and use units to solve problems.
C. Apply and extend previous understandings of numbers to the system of rational numbers.
D. Represent complex numbers and their operations on the complex plane.
E. Perform arithmetic operations with complex numbers.
F. Compute fluently with multi-digit numbers and find common factors and multiples.
G. Represent and model with vector quantities.
H. Perform operations on vectors.
I. Use properties of rational and irrational numbers.
J. Use complex numbers in polynomial identities and equations.
K. Extend the properties of exponents to rational exponents.
L. Know that there are numbers that are not rational, and approximate them by rational numbers.
M. Perform operations on matrices and use matrices in applications.
N. Apply and extend previous understandings of multiplication and division to divide fractions by fractions.


Thought: This problem involves understanding fractions, multiplication, and division.
Answer: A

Now, assign the following problem or activity to one or more relevant mathematical concepts/skills it teaches.
shot_info: fl_problem_001097

7
options: Draw, construct, and describe geometrical figures and describe the relationships between them.

Identify and describe shapes (squares, circles, triangles, rectangles, hexagons, cubes, cones, cylinders, and spheres).

Make geometric constructions.

Define trigonometric ratios and solve problems involving right triangles.

Draw and identify lines and angles, and classify shapes by properties of their lines and angles.

Understand congruence and similarity using physical models, transparencies, or geometry software.

Graph points on the coordinate plane to solve real-world and mathematical problems.

Explain volume formulas and use them to solve problems.

Visualize relationships between two-dimensional and three-dimensional objects.

Prove theorems involving similarity.

Classify two-dimensional figures into categories based on their properties.

Translate between the geometric description and the equation for a conic section.

Solve real-life and mathematical problems involving angle measure, area, surface area, and volume.

Reason with shapes and their attributes.

Solve real-world and mathematical problems involving area, surface area, and volume.

Apply geometric concepts in modeling situations.

Understand congruence in terms of rigid motions.

Experiment with transformations in the plane.

Understand and apply the Pythagorean Theorem.

Understand similarity in terms of similarity transformations.

Solve real-world and mathematical problems involving volume of cylinders, cones, and spheres.

Analyze, compare, create, and compose shapes.

Use coordinates to prove simple geometric theorems algebraically.

Apply trigonometry to general triangles.

Understand and apply theorems about circles.

Find arc lengths and areas of sectors of circles.

Prove geometric theorems.
problem_activity: Task
On graph paper, sketch a line segment with end points $A=(0,2)$ and $B=(0,6)$. Plot all points $C=(x,y)$ such that the triangle ABC has an area of 6 square units.
What two basic geometric theorems are needed to solve this problem?


correct_option_index: 22